polymorphic lambda-calculus

(Or "second order typed lambda-calculus",
"System F", "Lambda-2"). An extension of typed
lambda-calculus allowing functions which take types as
parameters. E.g. the polymorphic function "twice" may be
written:

twice = /\ t . \ (f :: t -> t) . \ (x :: t) . f (f x)

(where "/\" is an upper case Greek lambda and "(v :: T)" is
usually written as v with subscript T). The parameter t will
be bound to the type to which twice is applied, e.g.:

twice Int

takes and returns a function of type Int -> Int. (Actual type
arguments are often written in square brackets [ ]). Function
twice itself has a higher type:

twice :: Delta t . (t -> t) -> (t -> t)

(where Delta is an upper case Greek delta). Thus /\
introduces an object which is a function of a type and Delta
introduces a type which is a function of a type.

Polymorphic lambda-calculus was invented by Jean-Yves Girard
in 1971 and independently by John C. Reynolds in 1974.